Modelling and problem solving - quadratic equations

Can you please help me to answer the following question?

A pastry cook has decided to cook an octagonal cake, however he only has a square cake tin which is 24cm x 24cm x 7cm. He has decided to cut four rectangular pieces of cardboard, one for each corner, in order to make the interior of the tin octagonal. He wants the cake to be a regular octagon, and so the pieces of card must be just the right length. Find the size that each piece of cardboard must be to have the cake turn out as a regular octagon.